Advanced framework for assessment and reduction of model form uncertainty of the closure laws in thermal-hydraulics codes

Accurate modeling of the two-phase flow phenomena is important for the safety analysis of light water reactors. The modeling approach must balance model resolution with computational feasibility. The direct implementation of local instant formulation is not practical for most engineering applications. Two-phase two-fluid model is a time average formulation, where each phase is governed by separate set of conservation equations. The interactions between phases are modeled with interfacial terms present in the governing equations. The two-phase two-fluid model is a basis of many nuclear thermal-hydraulics codes used in design, licensing, and safety analysis of nuclear reactors. However, the averaging process introduces new turbulent and interfacial terms that require sub-grid models to close the system of equations. These closure laws describe the steady-state and dynamic characteristics of multi-phase media in terms of averaged field equations. The resolution required to model such terms is no longer a part of the system of equations, hence these closure laws must be derived by separate analysis. In a classical approach, semi-empirical correlations are derived based on direct observations from experimental investigation. However, with recent advances in data-driven techniques, a lot of attention was placed on using indirect experimental observations to improve the predictive capabilities of the closure laws. This work introduces a new methodology investigating modeling deficiencies using data-driven and statistical methods. Physics-discovered data-driven model form (P3DM) methodology uses a combination of reduced dimensionality modeling, data analysis and machine learning that aims at combining data-driven approaches with physics-based modeling. Model optimization is coupled to the solution of governing equations allowing model determination based on indirect observations of system response. The flexibility of the model form allows investigation of a large set of alternative models that are used to assess model form uncertainty. The methodology considers all limitations associated with the available data constraints encountered in the nuclear industry. The methodology uses the best features of calibration and machine learning type approaches while avoiding their limitations. Closure laws are associated with significant model form uncertainty. This uncertainty represents the lack of knowledge about modeled phenomena and is difficult to quantify. Bayesian model averaging is often used to assess model form uncertainty using competing, well-established models. However, alternative models suffer from similar assumptions, giving biased estimates of model form uncertainty. The P3DM methodology provides many alternative model forms. This set of possible models does not suffer from similar assumptions, giving an unbiased estimate of model form uncertainty. P3DM methodology was used to improve the modeling of the closure laws for the CTF subchannel code. The model correction was determined based on a substantial experimental database for 6 closure models. The correction term significantly improved the predictive capabilities of the CTF code. P3DM methodology was also used to assess the model form uncertainty of the TRACE system code in modeling of FTR phenomena. Under model form uncertainty estimated in this work, TRACE predicted FTR event for all validation experiments.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Nuclear, Plasma, Radiolgc Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2021

Author dc:creator

• Borowiec, Katarzyna

Contributors dc:contributor

• Kozlowski, Tomasz
• Brooks, Caleb
• Meidani, Hadi
• Uddin, Rizwan

• Two-fluid model
• Closure Laws
• Model Form Optimization
• P3DM
• Uncertainty Quantification
• Bayesian Analysis
• Model Form Uncertainty
• Two-Phase Flow

Statement dc:rights

• Copyright 2021 Katarzyna Borowiec

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/110808

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/110808